Structures of Metals

Because the metallic bond is nondirectional and because the positive ion cores attract each other through the intervening sea of electrons that flows between them, metals tend to form close-packed structures, meaning they try to get as dose together as they can in order to maximize their coordination nmnber. Johaimes Kepler (a mathematician as well as the famous astronomer) conjectured that the maximum number of identical spheres that could surround and touch another sphere was 12. Now, let us see what kinds of structures are possible with a coordination number of 12. 

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Gordon J G, Melroy O R and Toney M F 1995 Structure of metal-electrolyte interfaces copper on gold(111), water on silver(111) Electrochim. Acta 40 3-8... 

V. K. Grigorovich, The Metallic Bond and the Structure of Metal.s Nova Science, Huntington, NY (1989). 

W. B. Pearson, Handbook oJEattice Spacings and Structures of Metals and Alloys, International Series on MetalPhysics and Physical Metallurgy, Pergamon Press, New York, 1958, p. 130. 

J. R. Anderson, Structure of Metallic Catalysts, Academic Press, New York, 1975. 

Barrett, C.S. and Massalski, T.B. (1966) Structure of Metals crystallographic methods, principles and data, 3rd edition. Chapters 11 and 18 (McGraw-Hill, New York). The first and second editions appeared in 1943 and 1952, under Barrett s sole authorship. 

Hume-Rothery (1936) The Structure of Metals and Alloys (The Institute of Metals, London). 

The structures of metal-rich borides can be systematized by the schematic arrangements shown in Fig. 6.6, which illustrates the increasing tendency of B atoms to catenate as their concentration in the boride phase increases the B atoms are often at the centres of trigonal prisms of metal atoms (Fig. 6.7) and the various stoichiometries are accommodated as follows ... 

O.K. Andersen, O. Jepsen, and D. Glotzel, Canoi- al Description of the Band Structures of Metals, in Highlights of Condensed-Matter Theory, edited by F. Bassani, F. Fumi, and M.P. Tosi, North Holland, New York (1985). 

The corrosion of metals invariably involves some kind of interaction between a metal and its environment, and in many cases the corrosion (location, form and rate) is significantly affected or even caused by some structural feature of the metal. It is essential, therefore, for the corrosion engineer to have some appreciation of the structure of metals, and an elementary survey is provided in this section which provides a basis for an account of metal structure in relation to corrosion that is the subject of Section 1.3. 

A crystal may be defined as an orderly three-dimensional array of atoms, and all metals are aggregates of more or less imperfect crystals. In considering the structure of metals, therefore, it is convenient to start with the arrangement of atoms in a perfect metal crystal and then to proceed to the imperfections which are always present in the crystal structure. 

In this section the electronic structure of metal/polymcr/metal devices is considered. This is the essential starting point to describe the operating characteristics of LEDs. The first section describes internal photoemission measurements of metal/ polymer Schottky energy barriers in device structures. The second section presents measurements of built-in potentials which occur in device structures employing metals with different Schottky energy barriers. The Schottky energy barriers and the diode built-in potential largely determine the electrical characteristics of polymer LEDs. 

Table 21-IV shows some properties of the metals and their crystal forms. Since different crystal forms are involved in the series, trends in the properties are obscured. Figure 21-2 shows scale representations of the crystal structures of metallic beryllium, calcium, and barium.

X-ray diffraction studies on the structures of metal complexes in solution. H. Ohtaki, Rev. Inorg. Chem., 1982,4,103-177 (223). 

Coordinating properties of the amide bond. Stability and structure of metal ion complexes of peptides and related ligands. H. Sigel and R. B. Martin, Chem. Rev., 1982, 82, 385-426 (409). 

The analysis in this chapter has shown that during the past 10-15 years there have been only marginal modifications in our understanding of the structure of metal/solution interfaces based on the potential of zero charge. The general picture for the relative behavior of the various metals seems well established. In particular, new, more reliable data, where available, have confirmed trends already identifiable in a more ambiguous situation. 

Almost all that is known about the crystal face specificity of double-layer parameters has been obtained from studies with metal single-crystal faces in aqueous solutions. Studies in nonaqueous solvents would be welcome to obtain a better understanding of the influence of the crystallographic structure of metal surfaces on the orientation of solvent molecules at the interface in relation to their molecular properties. 

In recent years it has become clear that the structure of metals and alloys may be described in terms of covalent bonds that resonate among the alternative interatomic positions in the metals, and that this resonance is of greater importance for metals than for substances of any Other class, including the aromatic hydrocarbons. Moreover, the phenomenon of metallic resonance of the valency bonds must be given explicit consideration in the discussion of metallic valency it is necessary in deducing the metallic valency from the number of available electrons and bond orbitals to assign to one orbital a special r le in the metallic resonance. 

The indication from interatomic distances that less than 4 bonding electrons per atom are operating in white tin has been recognized by W. Hume-Rothery, The Structure of Metals and Alloys/ The Institute of Metals Monograph and Report Series No. 1, p. 26... 

In the course of the further investigation of resonating valence bonds in metals the nature and significance of this previously puzzling unstable orbital have been discovered, and it has become possible to formulate a rational theory of metallic valence and of the structure of metals and intermetallic compounds. 

A transargononic structure for sulfur, with six bonds formed by sp3d2 hybrid orbitals, was suggested for sulfur in the octahedral molecule SF6 long ago, and also for one of the sulfur atoms, with ligancy 6, in binnite (Pauling and Neuman, 1934). Some transargononic structures of metal sulfides have been proposed recently by Franzen (1966). 

The generally accepted theory of electric superconductivity of metals is based upon an assumed interaction between the conduction electrons and phonons in the crystal.1-3 The resonating-valence-bond theory, which is a theoiy of the electronic structure of metals developed about 20 years ago,4-6 provides the basis for a detailed description of the electron-phonon interaction, in relation to the atomic numbers of elements and the composition of alloys, and leads, as described below, to the conclusion that there are two classes of superconductors, crest superconductors and trough superconductors. 

The resonating-valence-bond theory of the electronic structure of metals is based upon the idea that pairs of electrons, occupying bond positions between adjacent pairs of atoms, are able to carry out unsynchronized or partially unsynchronized resonance through the crystal.4 In the course of the development of the theory a wave function was formulated describing the crystal in terms of two-electron functions in the various bond positions, with use of Bloch factors corresponding to different values of the electron-pair momentum.5 The part of the wave function corresponding to the electron pair was given as... 

The task of predicting a reasonable structure for this alloy was carried out with no information about the powder X-ray diffraction pattern except that one group of investigators had said that it could not be indexed by any Bravais lattice. The prediction of the structure was made entirely on the basis of knowledge of the effective radii of metal atoms and the principles determining the structure of metals and intermetallic compounds. 

The X-ray absorption fine structure (XAFS) methods (EXAFS and X-ray absorption near-edge structure (XANES)) are suitable techniques for determination of the local structure of metal complexes. Of these methods, the former provides structural information relating to the radial distribution of atom pairs in systems studied the number of neighboring atoms (coordination number) around a central atom in the first, second, and sometimes third coordination spheres the... 

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